CC BY
34
Section 9. Electrical engineering
DOI: http://dx.doi.org/10.20534/AJT-16-11.12-89-94
Baghdasaryan Marinka, National Polytechnic University Of Armeni, Professor, Doctor of Department of Electrical Engieenering, E-mail: m.baghdasaryan@seua.am Avetisyan Artem, National Polytechnic University of Armeni, Ph. D., Research Associate, E-mail: artemavetisyan83@gmail.com Alaverdyan Sonik, National Polytechnic University Of Armeni, Ph. D., assistant of Department of Electrical Engieenering, E-mail: sona.alaverdyan@yandex.ru
Developing the mathematical model for investigating the ore mill electric drive system
Abstract: The necessity of comprehensive consideration of the operation modes of the ore mill drive synchronous motor is substantiated by means of studying the change of its internal d angle. A mathematical model for investigating the dynamic phenomena of the ore mill drive system is proposed, allowing to study the dynamics of operation modes of drive motors of different mills, under the conditions of the change in the supply voltage and the load moment.
Keywords: mathematical model, synchronous motor, operation modes, ore mill.
Introduction. Ore grinding is the main process of system operation is considered exclusively from the
ore beneficiating enterprises, some construction and standpoint of the mill operation modes [1-2], while in
chemicals productions and has an important role in the others — by the characteristics of electric drive mo-
raising the labour efficiency in those production enter- tors consisting of the electromechanical system, control
prises. The implementation of that technological process equipment, and the mechanisms transmitting the power
by high technical and economic criteria can be ensured from the motor to the mill [3-4]. by providing a stable and reliable operation of power- The analysis of the well-known works devoted to
ful electric drive systems used in them. Considering the investigation and improvement of the operation
the abovementioned, and also the fact that the solution modes of the electric drive system ensuring the ore
of the problems aimed at raising the efficiency of the grinding shows that unique methods for investigating
ore-grinding process can be an important incentive for the operation modes have been developed by different
raising the productivity of mine-beneficiating and con- authors and significant theoretical experimental investi-
struction enterprises, the development of the method gations have been carried out.
for investigating the electromechanical system used in At the same time, it should be mentioned that the
that process is urgent. well-known experimental and theoretical materials do
Statement of the problem. The works aimed at in- not take into account the characteristics peculiar to the
vestigating the electric drive system ensuring the ore electromechanical system mill — motor, in particular,
grinding can be classified into two groups. In some of the dynamic behavior of the load, the possibilities of fall-
them, the study and improvement of the electric drive ing out of the synchronous mode during operation, the
random nature of the process. Besides, it is impossible to apply the traditional methods for investigating the operation modes of the electric drive system connected with the change in the technical and economic requirements of the ore-grinding process. That is why it is expedient to consider the problem of investigating and improving the operation modes of the electric drive system providing the ore grinding from a new standpoint. This can be implemented by applying well-known materials, revealing new opportunities, and developing a research model of the operation mode, which is the goal of this work. The peculiarity of the ore-mill electric drive is conditioned by the existence of relationship between the electromechanical phenomena of the drive and the technological process of ore grinding.
Regardless of the form of the electric drive used, the qualitative and quantitative characteristics of the finished product (ground ore) characterizing the operation of the system are conditioned by the operation states of the ore mill, the motor, control devices and the mechanisms transmitting the power from the motor to the mill. It can also be confirmed by the complete active power formed on the rotational axis of the mill drum [5]. The complete active power consumed by the mill drive motor is used for putting the active load of the mill into motion and a number
of losses and is determined by expression (1) [6]:
P + P
P = (1)
nDnM
where nD is the motor efficiency; nM - the efficiency of the drive mechanism transmission, allowing to consider the drive mechanism losses in the crown gear, in the clutch; Po - the useful power; Pn - the loss power.
Taking into account (1) and the formula of determining the motor power, we will obtain:
P + P
mlU costy = —--P-, (2)
nDnM
where m is the number of phases; I - the stator current; U - the supply voltage of the network; cos^ - the power coefficient.
Taking into account (2) and using the circular diagram of the synchronous motor, graphical dependencies between the electrical parameters of the motor and the filling degree ofthe ground material (Kh) (Fig. 1) have been confirmed. The cos0 = f(K„), sinp = f(Kh), I = f(K„) dependencies have been obtained by measuring the electrical parameters of the DC-260-38-36 motor used for the core mill drive by special sensors. From Fig. 1 it follows that the most sensitive is the curve sin^.
Considering the dependence cos^ = f (Kh) and the dependence obtained for the angle 0
0 = arctg
I cos0
+1 cos0
the change in the angle 0 conditioned by the change of the mill filling degree can be estimated. I, A cosq> sijicp
ISO 1401201003060504020
-1
-0.9
-0.6 -0.3
-0.3
—0.25 -0.2 —0.15 0.1
—0,05
A-3
J
Kk.%
20
I
40
~T 60
Fig. 1. The dependencies of the electrical parameters of the mill drive electric motor on the filling degree of the intra-mill load (Kh). 1 - the dependence of the stator current on the filling degree of the load;
2 - cosp = f (Kh); 3 - sinp = f (Kh)
Many works investigating the 0 = f (t) dependence of the synchronous motor are known [7], but they limit themselves only by confirming the dependence d = f (t) of the synchronous machine to study its fluctuations, and the change of the angle 0 by A0 is considered in relation to its constant value 00: 0 = 00 + Ad.
Respectively, the following dependence is used for the ME electromagnetic moment, which is a function from the angle 0
ME = MEo +Ame . Such investigations cannot estimate the motor operation mode dynamics ensuring the mill electric drive under the conditions of the qualitative and quantitative characteristics of the supplied ore and the voltage change.
Developing an investigation model for the ore mill electric drive system. For developing the investigation models for the operation modes of the ore mill electric drive system motor, the ratio characterizing the dependence of the mechanical characteristics of the motor and the mill is used:
MD = M - Mc, (3)
where M is the synchronous motor moment; Mc - the moment of resistance of the ore mill; MD - the dynamic moment of the drive system, depending on the system's moment of inertia [8] and is determined in the following way:
M D = T*,
D m ]
dt
(4)
where Tm is the constant of inertia; s - the slide.
The synchronous motor moment is determined [9]:
M =
mUEf sind mU2 sin 2d
(
x m
a
1 1
v
(5)
where m is the number of phases, U - the phase voltage applied to the stator winding; Ef - the excitation electromotive force; 9 - the phase shift angle between the main electromotive force and the network voltage vectors; xd -the inductive resistance ofthe stator phase according to the longitudinal axis; xq - the inductive resistance of the stator phase according to the cross section axis; a - the angular velocity ofthe motor. Mc is the moment of resistance of the ore mill and is determined in the following way:
Mc = mc f^cisin«, (6)
And if we bring it to the motor, we will obtain:
m c = m gR0
Vm®
-sina,
(7)
where ac is the angular velocity of the mill rotation; g - the free fall acceleration, nM - the efficiency of transmission from the motor shaft to the mill drum; a - the detour angle of the material in the mill; R01 - the 001 distance (Fig. 2); mc - the mass of the material ground in the mill.
The üüj distance is determined [9] by:
. 5 1
2R sin3-
R01 -
i 1 . 1 1
31--sin—cos—
2 2 2
(8)
where A is the central angle of the sector corresponding to the filling degree of the material in the mill (Fig. 2); R - the radius of the mill drum.
Fig. 2. A scheme for determining the moment of resistance of the ore mill
The mass of the material ground in the mill is deter mined [9] by:
yLR2
m =-
-(A- sin A),
(9)
where y is the volumetric density of the ground material; L - the length of the mill drum.
Placing equations (4), (5) and (7) in (3), we will obtain [10]:
T — = mdt =
mUEt sin0
(
+ mU2 sin 20
V
1 1
\\
V Xi Xd J J
-mc gR0
-sina
Expressing the a by the slide s and the angular velocity of synchronous rotation ac, we will obtain:
^ ds T — = mdt
V
mUEf sin0
---+ mU2 sin 20
x.
f W
' 1 1
V X9 Xd J J
1 + s r, mc (1 + s) .
x--mcgR01 —--- sin a
, (10)
from which:
^ ds T — = mdt
mUE( sin0
(
+ mU2 sin 20
1 1
\\
v
v xq Xd J J
r, °°cs ■ -mc gR0, —— sina +
Vm®
(11)
(
mUEt sin0
(
+ mU2 sin 20
1 1
\\
V Xq Xd J J
1
®
-mc gR0
Vm®
de
-sina.
Considering that s = —— and performing some mod-dt
ifications, we will obtain:
//
T
dt2
mUEf sin0
-f-+ mU sin20
1 1
V Xq Xd J J
-mc gK
mUEf sin0
-f-+ mU sin20
-sina
1 1
V Xq Xd ) )
W
d0
+
dt (12)
-mc gR01-— sin«.
Vm®
To investigate the state of the system in different operation modes by (12), the MatLab software package has been used. To construct the model, expression (12) is introduced by basic units:
x
d9 _ 1
dt2 _ TB
( f
mUEf sin 9
-f-+ mU2 sin 29
\\
1 1
V xq Xd J J
1 n ac ■ --mcgR01~^ Sina
a na
d9 dt
+
+
_ GD2n jp
where =-¡=-
mM 3450^3 40 • UI
mUEf sin 9
-f-+ mU sin29
V "d
2.„3_
f \ \
1 1 1
X X, a
V q "J J
a
sina
B y[?>UIp cy of synchronous rotation; p - the number of synchro-
, m ' nous motor stator pair of poles; I - the stator current.
GD2 is the rotor's acceleration torque; n - the frequen- The model for estimating the electric drive motor
operation in different operation modes is shown in Fig. 3.
Fig. 3. The block-diagram of the model for estimating
The calculation block of the "From1" components of the model introduced in Fig. 3 is presented in Fig. 4.
By the results "From1" of testing the developed model, the changes of the 0 angle have been constructed at different values of the mill load mass ((m'<m"c)) (Fig.5) and at different values of efficiency of the rotation moment transmitting from motor shaft to the mill drum (n'L<nM ) (Fig. 6). As it can be seen from the characteristics, both in case of an increase in the load mass and a decrease in the transmission efficiency, the amplitude values of the angle 0 turn out more conditioned by the growth of the resistance moment.
the operation of the electric drive motor of ore mill
Conclusion
A model for investigating the dynamic phenomena of the ore mill synchronous drive system is developed enabling to study the dynamics of drive motors operation modes of different mills under the conditions of changing supply voltage and load moment. The application of the proposed model can be the basis for increasing the electric drive system reliability and improvement of the start-up modes.
Fig. 4. Calculation schemas a) Calculation schema of "Froml" component; b) Calculation schema of the "From2" component included in "Froml" component
Fig. 5. Dependence of the change of angle 9 on time at different load masses (m'c < m'')
Fig. 6. Dependence of the change of angle 9 on time at different efficiencies of transmission (V^n'M)
References:
1. Pending patent 2304438 (RF). Automated control device for the ore crushing process./B. B. Bnin, V. M. Kurkin, V. A. Borovkov, A. G. Marodadki, V. M. Leushin. - Publ. in Proceedings. - 2003. - N14. (in Russian).
2. Schnatz R., Int. J. Miner. Optimization of continuous ball mills used for finish-grinding of cement by varying the L/D ratio, ball charge filling ratio, ball size and residence time//Process. - 2004. - N1. - P. S. 55; - S. 63.
3. Kuvaev Ya. G. Automated expert energy-saving control system with exclusive cycle ofwet ball grinding.//Naukovo, Practical journal. - 2006. - No 3, URL: htt://www.nas.gov.ua/scinn/pages/uu03060.html
4. Fomin D.V. Investigation of the automated system of synchronous motor stimulation in the function of load angle. // Electromechanics. 2004. - N 2. - P. 79-81.
5. Guide on ore beneficiation. Preparatory processes/Under edition O.S. Bogdanov. - I.: Nedra, 1982. - 336 p.
6. Guide on ore beneficiation/ G. I Adamov, V.A. Annushkina - I.: Nedra, 1984. - 358 p. (in Russian)
7. M.G. Chilikin, A.S. Sandler. Guidelines of electric drive. - M.: Energoizdat. 1981. - 576 p.
8. Kopilov I. P. Electrical machines. - M.: Visshaya shkola. 2006. - 607 p.
9. Maryuta A.N. Model of friction vibrations of the central part of the drum mills//Proceedings of HEE. Mining Journal. 1985. - N3. - P. 106-112.
10. Avetisyan A.M. Model of investigating the dynamic processes of the ore-grinding mill electromechanical system by applying MATLAB software package//SEUA Proceedings -75: Collection of scientific and methodic articles. Yerevan. - 2008. - P. 115-118.
